SNAP Spacecraft Orbit Design

1. SNAP Spacecraft Orbit Design Stanford University Matthew Peet

2. Presentation Layout • Mission requirements • The use of swingby trajectories • Previous research • Research goals • Status of current work • Plans for future work

3. SNAP Mission Requirements • Minimize Accelerations • Improves target tracking • Minimize length of eclipse duration • Reduces onboard battery requirements • Weight(~1kg/kW-hr) • complexity • Heating and standby power reduced • Maximum contact with Berkeley • Allows increased data download • Improves control ability and reaction time • Avoid radiation belts

4. Candidate Orbit Types Low Earth Orbit Geostationary Orbit High Earth Orbit Lagrange Orbit

5. Preferred Orbit Design • High earth orbit • High inclination to avoid eclipse • >35 degrees required to avoid moon, but higher is better • Moderate eccentricity • Rp > 8 Re to avoid radiation • Ra < Rm to reduce antenna power • Apogee over northern hemisphere

6. Launch Requirements • For direct injection • three burns required for a total delta-v of 12 km/s • 1.75 km/s worth of fuel onboard for final burn • 2200 lbs of fuel for a 2000 lb spacecraft • Delta II Class Launch Vehicle Needed • Upper Stage Required • Cost: 80M-100M

7. Uses the gravitational attraction of a planetary body to alter the motion of a satellite. Rotates relative spacecraft velocity in the planet-fixed reference frame about axes fixed to the planet. Satellite energy is conserved within the planetary reference frame. Planet-fixed frame is in motion with respect to the inertial space A rotation in planetary system may not result in satellite energy conservation in inertial space Gravity Assists

8. Swingby trajectories • Path of the spacecraft in planetary reference frame is rotated by angle delta • Sin(/2) = 1/e • e = 1 - Rp/a • a = 2*/v2

9. Previous Research • History of swingby trajectories in interplanetary mission design • Voyager, Pioneer, Magellan, Galileo, Cassini • Prometheus mission concept development • Long term observation strategy • Communications satellite rescue mission • Provided inclination change for stranded geostationary satellite

10. Interplanetary Mission Design • First uses of Swingby concept • Restricted to in-plane maneuvers • No inclination changes • Allows for simplification • Voyager and Apollo through Cassini

11. Prometheus Mission Concept • 1985 - current • First exploration of swingby trajectories for near-earth applications • Inclination changing • Perigee raising • Utilized a Monte-Carlo style technique • Never launched

12. Satellite Rescue Mission Analysis • 1998 - current • Development of technique for multiple passes • Insufficient fuel resources for direct encounter • Derivative based solution developed by Cesar Ocampo et al.

13. Goals of Current Research • Reduce launch costs by minimizing the delta-v required to place the SNAP satellite in its optimal orbit • Facilitate mission planning by developing an analytic process that will produce an optimal lunar assist trajectory given launch date and desired orbit • Improve the analytical process to provide long-term orbit stability

14. Status of Current Research • Developed baseline trajectory based on adaptations of historical mission plans • Developed first order method for prediction and control of lunar encounter • Improved baseline trajectory based on analytical predictions

15. Baseline Trajectory • Launch: October 20, 2007 • Based on Prometheus mission design • Earth observation satellite mission • Lunar intersection occurs at descending node • Eases adaptation of orbit

16. Used STK with Astrogator to propagate orbit Used 12th order earth model with perturbations out to 1/3 lunar distance Runge-Kutta variable step propagator Used 4th order selenocentric model with earth point mass and perturbations during lunar encounter CisLunar variable step propagator Used Initial trajectory identical to Prometheus mission Calculated relative phase of moon in orbit at intersection during old mission Calculated next occurrence for this phase starting in October, 2007 Determined launch date and time to intercept moon at this point in time Development of Trajectory

17. Baseline Trajectory • Final Orbital Elements: • Rp = 11 Re • e = .696 • i = 55.3 deg • RAAN = 354.3 deg • AOP = 22.3

18. Development of Analytic Method • Consists of 3 stages • Intercept stage • Intercept stage • Swingby stage • Swingby stage • Return stage • Return stage

19. Intercept Stage • Relate launch conditions to arrival conditions at moon • Find launch conditions for a given set of arrival conditions • Include effects of phasing loops and determine launch windows for desired conditions

20. Calculate launch conditions given launch date and azimuth Calculate lunar position given intercept time Apply phasing loops, if any Propagate to lunar sphere of influence Uses proportional error control to converge on solution yields time of arrival and lunar position at arrival Calculate relative position and velocity of the craft with respect to the moon at arrival Given desired arrival conditions,relate back to specified launch conditions Assumes constant arrival time at sphere of influence work in progress Development of Intercept Stage

21. Swingby Stage • Within sphere of influence, use simplified 2 body orbital motion • Relate exit conditions to arrival conditions

22. Translate relative position and velocity into Keplerian elements describing the lunar encounter Propagate orbit through to edge of sphere of influence Transform relative position and velocity to the inertial frame Given beta-plane targeting parameters, calculate position and velocity at entrance to sphere of influence Given exit position and velocity, determine beta-plane targeting parameters The beta-plane parameters are used as outputs when the scenario is run through STK to ensure the values are roughly accurate Development of Swingby Stage

23. Return Stage • Relate elements of final orbit to sphere of influence exit conditions • Assume an apogee lowering burn at perigee to provide orbital stability

24. Given position and velocity at edge of lunar sphere of influence, calculate new orbital element Given new set of orbital elements, calculate apogee lowering burn for desired stability period ¼, ½, 2/3 lunar period, etc. Find the final orbital elements following final burn i and RAAN do not change e can be related directly to elements at exit efinal = 1-afinal(1-e)/a Given desired Earth-Vehicle-Moon(EVM) angle and orbital parameters, determine initial AOP not yet complete Verify that desired orbital parameters meet Tisserand Criterion Find exit position and velocity given desired orbital elements entirely analytic solution does not include mean or true anomaly Development of Return Stage

25. Improved Baseline Trajectory • Improved orbital characteristics • Rp = 20 Re • e = .399 • i = 73 deg • RAAN = 351 deg • AOP = 221.5 deg

26. High Inclination • Inclination of 73 degrees • Reduced eclipse time to 5.6 hours • Only 82 minutes in the umbra

27. Orbital Stability • Three year nominal stability • Intrinsic stability of semi-major axis due to lunar influence • Slight reduction of inclination over lifetime of spacecraft • Increase in eclipse time is small • This stability issue will be explored in future work

28. Orbit Stability

29. Coverage Time • Over the course of the three year lifetime • 60% is spent in Northern Hemisphere • 55.2% is spent in LOS contact with Bay Area

30. Launch Costs • On-board fuel reserves require only 90 m/s • only 78 lb of fuel required • Launch Vehicle requirements reduced • C3 of –2 km^2/s^2

31. Plans for Future Work • Orbital Stability Investigation • Improve Matlab models • Design semi-analytic tools similar to the Ocampo research